Guide mechanisms of the aforesaid kind are known to the art from, for example, German Patent Specification DE No. 960 882. It has been found, however, that with this known mechanism the fins are often extended much too slowly, resulting in insufficient muzzle stability of the projectile. The tail of the projectile is namely still influenced by the pressure exerted by the propellant gases (powder gases) even when the guide surfaces of the projectile have left the muzzle of the barrel, and uneven loads on the fins can therewith cause pronounced wobble or yaw of the projectile in the vicinity of said muzzle, resulting in impaired external ballistics and impaired precision. This problem is particularly difficult to overcome in the case of dart shaped or sweepback projectiles.